AP Statistics / Mr. Hansen
3/5/2003

Name: _________KEY___________

Happy Quiz on Chapter 9

1.

Suppose that the true proportion of registered voters in Springfield (pop. 3500) who support Mayor Quimby is 42.5%. In an SRS of 200 registered voters in Springfield, what is the probability that more than 80 support Quimby? Do this 3 ways:

 

 

(a)

Using a binomial approach for the count of 80;

 

 

 

Let X = # of voters favoring Quimby in SRS of 200

 

P(X > 80) = 1 – P(X £ 80) = 1 – .261 by calc. = .739

 

 

 

 

 

 

(b)

Using a normal-approximation approach for the sample proportion of .4;

 

 

 

 

 

 

 

 

 

(c)

Using a normal-approximation approach for the count of 80.

 

 

 

 

 

 

 

 

 

2.

Justify why parts (b) or (c) constitute a valid approach.

 

 

 

Pop. (est. 2000 registered voters) is at least 10n = 10(200) = 2000 Ž trials are nearly indep., close enough to be considered binom.ü

 

 

 

np = 200(.425) = 85 ³ 10ü

 

nq = 200(.575) = 115 ³ 10ü

 

(These last 2 rules of thumb verify that z approx. to binom. is valid.)

 

 

3.

STA students’ heights follow N(70, 2.5) (in inches). Find the probability that in an SRS of 30 students, the mean height exceeds 6 feet.